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We study the geometry underlying the Wilson loop diagram approach tocalculating scattering amplitudes in the gauge theory of Supersymmetric YangMills (SYM) $N=4$. By applying the tools developed to study total positivity inthe real Grassmannian, we are able to systematically compute with all Wilsonloop diagrams of a given size and find unexpected patterns and relationshipsbetween them. We focus on the smallest nontrivial multi-propagator case,consisting of 2 propagators on 6 vertices, and compute the positroid cellsassociated to each diagram and the homology of the subcomplex they generate in$\mathbb{G}_{\mathbb{R}, \geq 0}$. We also verify in this case the conjecturethat the spurious singularities of the volume functional {\em do} all cancel onthe codimension 1 boundaries of these cells.

A study in $\mathbb{G}_{\mathbb{R}, \geq 0}$: from the geometric case book of Wilson loop diagrams and SYM $N=4$